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Localization in quantum field theory (a review)

We review the localization issue in quantum field theory and detail the nonrelativistic limit. Three distinct localization schemes are examined: the Newton–Wigner, the algebraic quantum field theory, and the modal scheme. Among these, the algebraic quantum field theory provides a fundamental concept of localization rooted in its axiomatic formulation. In contrast, the Newton–Wigner scheme draws inspiration from the Born interpretation, applying mainly to the nonrelativistic regime. The modal scheme, relying on the representation of single particles as positive frequency modes of the Klein–Gordon equation, is found to be incompatible with the algebraic quantum field theory localization.
This review delves into the distinctive features of each scheme, offering a comparative analysis. A specific focus is placed on independence between state preparations and observable measurements in spacelike-separated regions. Notably, localization in algebraic quantum field theory violates this independence due to the Reeh–Schlieder theorem. Drawing parallels with the quantum teleportation protocol, it is argued that causality remains unviolated. Additionally, we consider the nonrelativistic limit of quantum field theory, revealing the emergence of the Born scheme as the fundamental concept of localization. Consequently,
the nonlocality associated with the Reeh–Schlieder theorem is shown to be suppressed under nonrelativistic conditions.


(see also Localization in Quantum Field Theory for Inertial and Accelerated Observers)

Deep Learning Enabled Transmission of Full-Stokes Polarization Images Through Complex Media

Polarization images offer crucial functionalities across multiple scientific domains, providing access to physical information beyond conventional measures such as intensity, phase, and spectrum of light. However, the challenge of transmitting polarization images through complex media has restricted their application in optical communication and imaging. Here, a novel approach utilizing deep learning for the transmission of full-Stokes polarization images through scattering media is presented. It is demonstrated that any input polarization image can be reconstructed in a single shot by employing only an intensity sensor. By supervised training of a deep neural network, high-accuracy full-Stokes reconstruction is achieved from the speckle pattern detected by an intensity camera. Leveraging the deep learning based polarization decoder, a polarization-colored encoding scheme is devised to enable increased-capacity data transmission through disordered channels. Fast, wavelength-independent, on-chip, polarization imaging in complex media enables the utilization of polarization-structured light in multimode fibres and opaque materials, unlocking new possibilities in optical communication, cryptography, and quantum technology.


Non-Gaussianity in the quantum parametric oscillator


Systems of coupled optical parametric oscillators (OPOs) forming an Ising machine are emerging as large-scale simulators of the Ising model. The advances in computer science and nonlinear optics have triggered not only the physical realization of hybrid (electrooptical) or all-optical Ising machines, but also the demonstration of quantum-inspired algorithms boosting their performances. To date, the use of the quantum nature of parametrically generated light as a further resource for computation represents a major open issue. A key quantum feature is the non-Gaussian character of the system state across the oscillation threshold. In this paper, we perform an ab initio analysis of the emergence of non-Gaussianity in the single quantum OPO with an applied external field. We model the OPO by a Lindblad master equation, which is numerically solved by a first-principles method based on exact diagonalization. Non-Gaussianity is quantified by means of three different metrics: the Hilbert-Schmidt distance, quantum relative entropy, and photon distribution. Our findings reveal a nontrivial interplay between parametric drive and applied field: (i) the increasing pump monotonically enhances non-Gaussianity and (ii) the increasing field first sharpens non-Gaussianity, and then restores the Gaussian character of the state when above a threshold value. We also report a first-principles computation in the Fock space of the distance from the mixture of coherent states, a strongly nonclassical behavior that can play a significant role in the quantum parallel search for optimization.

See also arXiv